The two justified prior densities derived above are consistent with the assumptions implicit in most approaches to the measure problem. The volume-weighted prior (REF )
is reflected in measures based on the late-time, quasi-stationary distribution [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
For this reason, we refer to this case as the late-time hypothesis \({\cal H}_{\rm late}\) . Meanwhile, the uniform prior (REF ) is representative of local measures [7]}, [8]}, [9]}, [10]}. It is also consistent with the early-time approach to eternal inflation [11]}, [12]}, [13]}, [14]}, [15]}, which postulates that we exist well-before the exponentially-long mixing time for the landscape.
We henceforth refer to this prior as uniform-time hypothesis \({\cal H}_{\rm uni}\) .
